Asked by BlUbArRy!2#

25.
The distance a spring will stretch varies directly with how much weight is attached to the spring. If a spring stretches 6 inches with 80 pounds attached, how far will it stretch with 55 pounds attached? Round to the nearest tenth of an inch.

Answers

There are no human answers yet.
Answered by GPT-4o mini
To solve the problem, we'll use the fact that the distance a spring stretches varies directly with the weight attached to it. This can be expressed with the equation:

\[
d = k \cdot w
\]

where:
- \( d \) is the distance the spring stretches,
- \( w \) is the weight attached to the spring,
- \( k \) is the constant of variation.

From the problem, we know that when \( w = 80 \) pounds, the spring stretches \( d = 6 \) inches. We can use this information to find the constant \( k \):

\[
6 = k \cdot 80
\]
\[
k = \frac{6}{80} = \frac{3}{40}
\]

Now that we have the value of \( k \), we can find how far the spring will stretch when \( w = 55 \) pounds:

\[
d = k \cdot w
\]
\[
d = \frac{3}{40} \cdot 55
\]

Calculating this value:

\[
d = \frac{3 \cdot 55}{40} = \frac{165}{40} = 4.125
\]

Now rounding to the nearest tenth, we get:

\[
d \approx 4.1 \text{ inches}
\]

Thus, the spring will stretch approximately **4.1 inches** with 55 pounds attached.

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